The adaptive index selection immediately results in many papers devoted to various aspects of the new algorithm [1]}, [2]}, [3]}, [4]}.
Li and Zhang gave a greedy block Gauss-Seidel method, where all the coordinates satisfy a greedy rule [2]}. Based on the block Kaczmarz iteration scheme [6]}, [7]} and a modified greedy row selection from [8]}, [9]}, the greedy block Kaczmarz (GBK) was proposed by Niu and Zheng [4]}. This method needs to calculate the Moore-Penrose pseudoinverse of the row submatrix. Several pseudoinverse-free methods can be found in [1]}, [2]}, [3]}. Recently, a fast deterministic block Kaczmarz (FDBK) method, according to the greedy criterion of row selections, was presented by Chen and Huang [14]}.
